Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
determine each segment length in right triangle abc
in the triangle: ∠c = 45°, ∠a = 45°, ad = 7, ca = 14
tiles: $14\sqrt{2}$, $14\sqrt{3}$, $7\sqrt{3}$, $7\sqrt{2}$, 7, 14
match:
$bd$ $\longrightarrow$
$bc$ $\longrightarrow$

Explanation:

Step1: Find length of CD

Given $CA=14$, $DA=7$.
$CD = CA - DA = 14 - 7 = 7$

Step2: Calculate length of BD

$\triangle BDA$ is 45-45-90 triangle, so $BD=DA$.
$BD = 7$

Step3: Calculate length of BC

Use Pythagorean theorem on $\triangle BCD$: $BC=\sqrt{CD^2+BD^2}$
$BC = \sqrt{7^2+7^2} = \sqrt{49+49} = \sqrt{98} = 7\sqrt{2}$

Answer:

$BD
ightarrow 7$
$BC
ightarrow 7\sqrt{2}$